A reliable vascular access is a critical requirement for providing adequate hemodialysis. The two types of permanent vascular access are an arterio-venous (A-V) fistula and an A-V graft. Grafts are prone to developing myointimal hyperplasia at the venous anastomosis, which leads to recurrent stenosis and thrombosis. A pharmacologic intervention that prevents myointimal hyperplasia might decrease the frequency of graft stenosis and thrombosis, thereby reducing the need for costly interventions and prolonging their long-term patency for dialysis. In vitro studies have demonstrated that the anti-platelet agent dipyridamole inhibits vascular smooth cell proliferation. Moreover, a single-center, randomized, double- blinded clinical trial observed that dipyridamole (with or without aspirin) decreased the frequency of graft thrombosis by 40-50%. Fistulas are preferred to grafts for vascular access. Once fistulas are successfully used for dialysis, they require far fewer interventions to achieve long-term patency, as compared with grafts. However, fistulas have a high (approximately 35%) rate of primary failure (fistulas that are never usable for dialysis). Primary failure may be due to early thrombosis or failure to mature. Early fistula thrombosis may result from a hyper-coagulable state due to vascular injury following surgery. For this reason, short-term treatment with an anti-platelet agent may reduce the frequency of early fistula thrombosis. Small pilot studies have shown that ticlopidine, sulfinpyrazone, and aspirin may prevent early fistula thrombosis. The proposed study will consist of 2 parallel prospective, randomized, double-blinded, multi-center investigations. In the first one, chronic kidney disease patients receiving a new A-V graft will be randomized to receive either Aggrenox (long-acting dipyridamole + low-dose aspirin) or placebo twice daily. The primary endpoint will be intervention-free graft survival. The second study will randomize patients receiving a new fistula to receive either clopidogrel 75 mg or placebo once daily. The primary endpoint will be fistula thrombosis within 6 weeks, and the secondary endpoint will be the ability to use the fistula successfully for dialysis within 6 months.